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A068025
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Z(S_m; sigma[1](n), sigma[2](n),..., sigma[m](n)) where Z(S_m; x_1,x_2,...,x_m) is the cycle index of the symmetric group S_m and sigma[k](n) is the sum of k-th powers of divisors of n; m=8.
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2
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1, 511, 9841, 174251, 488281, 6017605, 6725601, 50955971, 72636421, 276964061, 235794769, 2234070293, 883708281, 3698977205, 5148057541, 13910980083, 7411742281, 46982039533, 17927094321, 99343345101, 69493620405
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OFFSET
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1,2
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LINKS
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FORMULA
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1/8!*(sigma[1](n)^8 + 28*sigma[1](n)^6*sigma[2](n) + 112*sigma[1](n)^5*sigma[3](n) + 210*sigma[1](n)^4*sigma[2](n)^2 + 420*sigma[1](n)^4*sigma[4](n) + 1120*sigma[1](n)^3*sigma[2](n)*sigma[3](n) + 420*sigma[1](n)^2*sigma[2](n)^3 + 1344*sigma[1](n)^3*sigma[5](n) + 2520*sigma[1](n)^2*sigma[2](n)*sigma[4](n) + 1120*sigma[1](n)^2*sigma[3](n)^2 + 1680*sigma[1](n)*sigma[2](n)^2*sigma[3](n) + 105*sigma[2](n)^4 + 3360*sigma[1](n)^2*sigma[6](n) + 4032*sigma[1](n)*sigma[2](n)*sigma[5](n) + 3360*sigma[1](n)*sigma[3](n)*sigma[4](n) + 1260*sigma[2](n)^2*sigma[4](n) + 1120*sigma[2](n)*sigma[3](n)^2 + 5760*sigma[7](n)*sigma[1](n) + 3360*sigma[2](n)*sigma[6](n) + 2688*sigma[3](n)*sigma[5](n) + 1260*sigma[4](n)^2 + 5040*sigma[8](n)).
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MATHEMATICA
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CIP8 = CycleIndexPolynomial[SymmetricGroup[8], Array[x, 8]]; a[n_] := CIP8 /. x[k_] -> DivisorSigma[k, n]; Array[a, 21] (* Jean-François Alcover, Nov 04 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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